Ideal of hypercyclic operators that factor through $\ell ^p$

2021 ◽  
pp. 1
Author(s):  
Asuman Güven Aksoy ◽  
Yunied Puig
Keyword(s):  
Hypercyclic Operators

scholarly journals On hypercyclicity and supercyclicity criteria

2004 ◽  
Vol 70 (1) ◽  
pp. 45-54 ◽  
Author(s):  
Teresa Bermúdez ◽  
Antonio Bonilla ◽  
Alfredo Peris
Keyword(s):  
Wide Class ◽  
Hypercyclic Operators ◽  
Dense Range ◽  
Hypercyclicity Criterion ◽  
Supercyclicity Criterion

We show that the Hypercyclicity Criterion coincides with other existing hypercyclicity criteria and prove that a wide class of hypercyclic operators satisfy the Criterion. The results obtained extend or improve earlier work of several authors. We also unify the different versions of the Supercyclicity Criterion and show that operators with dense generalised kernel and dense range are supercyclic.

scholarly journals Topologically mixing hypercyclic operators

2003 ◽  
Vol 132 (2) ◽  
pp. 385-389 ◽  
Author(s):  
George Costakis ◽  
Martín Sambarino
Keyword(s):  
Hypercyclic Operators ◽  
Topologically Mixing

scholarly journals Hypercyclic operators on algebra of symmetric analytic functions on $\ell_p$

2016 ◽  
Vol 8 (1) ◽  
pp. 127-133 ◽  
Author(s):  
Z.G. Mozhyrovska
Keyword(s):  
Analytic Functions ◽  
Entire Functions ◽  
Composition Operators ◽  
Translation Operator ◽  
Hypercyclic Operators ◽  
Polynomial Automorphisms ◽  
Fréchet Algebra

In the paper, it is proposed a method of construction of hypercyclic composition operators on $H(\mathbb{C}^n)$ using polynomial automorphisms of $\mathbb{C}^n$ and symmetric analytic functions on $\ell_p.$ In particular, we show that an "symmetric translation" operator is hypercyclic on a Frechet algebra of symmetric entire functions on $\ell_p$ which are bounded on bounded subsets.

scholarly journals Some questions about subspace-hypercyclic operators

2013 ◽  
Vol 408 (1) ◽  
pp. 209-212 ◽  
Author(s):  
R.R. Jiménez-Munguía ◽  
R.A. Martínez-Avendaño ◽  
A. Peris
Keyword(s):  
Hypercyclic Operators

scholarly journals Hereditarily hypercyclic operators and mixing

2007 ◽  
Vol 330 (1) ◽  
pp. 237-244 ◽  
Author(s):  
Enhui Shi ◽  
Yuwu Yao ◽  
Lizhen Zhou ◽  
Youcheng Zhou
Keyword(s):  
Hypercyclic Operators
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